Previous investigations in the Biological Response Modifiers Program and elsewhere have demonstrated significant activity of recombinant alpha interferon in patients with relapsed favorable histology non-Hodgkin's lymphoma and in some patients with diffuse poorly differentiated lymphoma. Most patients entered on this trial, however, require dose reductions because of excessive toxicity. Studies done concurrently with the initial lymphoma studies at other institutions demonstrate significant activity of very low doses of recombinant alpha interferon in patients with hairy cell leukemia, another chronic B-cell neoplasm. The purpose of the current trial was to determine if patients with favorable histology, non-Hodgkin's lymphoma would respond to the lower doses of interferon found to be very effective in patients with hairy cell leukemia. A second objective of the trial was to further evaluate the efficacy of high dose recombinant alpha interferon in patients with diffuse poorly differentiated lymphoma since only small numbers of these patients had been treated in the intial trial. The third objective of the trial was to attempt to determine if low doses of recombinant alpha interferon would be effective in patients with the recently described T gamma lymphoproliferative disorder, a disorder of T cells that resembles in many regards hairy cell leukemia.